This looks to solve those two issues.
Step 1: Materials
1 3 Ft. x 18 In. Board
4 NON Pivoting Wheels
2 Pivot Hinges
2 3 In. Pin Locks
Cutting Implement (I used a miter saw)
Step 2: Basic Assembly
I didn't want the hole to be too big as it would have to carry considerable weight when rolling the full bin around, however, I wanted it to be big enough to get a rake or shovel into.
Attach the top edge of the door with 2 hinges, and then use the pin locks on the bottom edge. Make sure to place the locks on the side (parallel to the ground). I mistakenly placed them vertically along the bottom and when the barrel flexed, the door popped open every time.
Step 3: The Platform
Screw the 4 wheels about 2-4 inches in from the top and bottom. this lets the groove of the barrel keep it on the wheels.
Don't place the wheels too close to the middle, you don't want them hitting the door or door hardware (ask me how I know!).